Serena Williams and Maria Sharapova easily reached the third round of the Qatar Open, dominating their opponents with straight-set victories.

Williams, who will regain the No 1 ranking if she reaches the semi-finals, showed no signs of the back or ankle problems that troubled her at the Australian Open during her 6-2, 6-1 win over Russian qualifier Daria Gavrilova.

The third-ranked Sharapova, who won the tournament in her two previous appearances, downed French qualifier Caroline Garcia 6-3, 6-2. Sixth-ranked Angelique Kerber had a much tougher time, though, and became the first top player to be eliminated from the tournament as she was routed by fellow German Mona Barthel 6-1, 6-2 in just over an hour.

Williams broke Gavrilova to go up 4-2 in the first set and then jumped out to a 5-0 lead in the second.

Williams then saved five break points before serving out the match when the 160th-ranked Gavrilova hit a forehand long.

The 15-time Grand Slam winner said she was "happy to get out of it, get it over with" and said her ankle held up well.

"I have it heavily taped. As long as the tape doesn't get loose, it feels really good," Williams said. "Physically feeling better is so good, and hopefully I can stay on that level."

But Williams acknowledged she has to do better on her first serve, which is considered among the best in the world but was inconsistent against Gavrilova, hitting the mark just over half the time.

"I wasn't making my first serve today," she said. "It's always something I can work on and try to do better in my next round."

Sharapova broke the 172nd-ranked Garcia twice go up 3-0 in the first set. Garcia won the next two games but Sharapova then broke for a third time. The second set went with serve through the first five games until Sharapova broke to go up 4-2, and she clinched the victory when the Frenchwoman hit a forehand long.

"I was quite happy with the way I played, because my opponent has already played a few matches here so she's been able to get in that match atmosphere," Sharapova said. "So I wanted to start really strong. I had a tough match against her in my previous encounter where I played three sets. I really wanted to start better this time as opposed to last time."

Sharapova was joined in the third round by 11th-ranked Marion Bartoli, who downed former French Open champion Francesca Schiavone 7-6 (5), 6-3. The loss leaves Schiavone, who has fallen to 54th in the rankings, winless in four matches this year.

The Italian had the upper hand early, racing out to a 4-1 lead. But Bartoli turned things around, saving five break points to make it 4-2 breaking back in the next game when Schiavone doubled faulted. She then decided the tiebreaker with a return winner.

After trading breaks early in the second set, Bartoli took advantage of Schiavone's errors to go up 4-2. She closed out the match when she chased down a volley and fired a backhand winner down the line.

"The first set was extremely tough," Bartoli said. "It was a hard battle. I knew from coming from indoor clay court I wouldn't play my best tennis for the first 30 minutes. ... But I felt I really fought really hard on the court. I didn't show any frustration."

Kerber broke Barthel to start the match but couldn't win another game in the first set.

Barthel, who won her second singles title at the Open Gaz de France Suez this month, finished with 30 winners and only 12 unforced errors for her fourth win over a top-10 player

Sloane Stephens, the 17th-ranked American who beat Williams in the Australian Open quarterfinals, defeated Anna Tatishvili of Georgia, 6-2, 6-2.

No. 12 Maria Kirilenko of Russia retired with a right shoulder injury against fellow Russian Ekaterina Bychkova after falling behind 3-0. Yanina Wickmayer of Belgium also withdrew from the tournament with a lower back injury, as did Varvara Lepchenko of the United States with an upper respiratory illness.